Problem 53 - College Algebra

Question

In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind pressure is a measure of a hurricane's destructive capacity, what happens to this destructive power when the wind speed doubles?

Step-by-Step Solution

Answer

If the wind speed doubles, the destructive capacity, represented by wind pressure, quadruples.

Step 1: Understand the problem

The problem states that the wind pressure varies directly as the square of the wind velocity. Therefore, the formula given for the relationship between pressure and velocity is \( P = kV^2 \). We need to figure out how the pressure changes when velocity doubles.

Step 2: Substitute the new value of velocity

If the wind speed doubles, that means the new velocity is \( 2V \). We substitute this into our formula, leading to \( P' = k(2V)^2 \) where \( P' \) is the new pressure.

Step 3: Simplify and analyze the result

We simplify the equation to \( P' = k \cdot 4V^2 \). This equation tells us that quadrupling the wind speed will quadruple the wind pressure. This means the destructive power of a hurricane quadruples every time the wind speed doubles.